Question

Pablo drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Pablo drove home, there was no traffic and the trip only took 4 hours. If his average rate was 40 miles per hour faster on the trip home, how far away does Pablo live from the mountains?

Answer 1

Using the relation between velocity, distance and time, it is found that Pablo lives 288 miles away from the mountains.

What is the relation between velocity, distance and time?

• Velocity is distance divided by time, that is:

$v = \frac{d}{t}$

Going to the mountain:

• Velocity v.

• Distance d.

• Time of 9 hours, hence $t = 9$.

Then, considering we want the distance:

$v = \frac{d}{t}$

$v = \frac{d}{9}$

$d = 9v$

$v = \frac{d}{9}$

Returning from the mountain:

• 40 miles per hour faster on the trip home hence the velocity is v + 40.

• Distance d.

• Time of 4 hours, hence $t = 4$.

Then:

$v + 40 = \frac{d}{4}$

$d = 4v + 160$

Since $v = \frac{d}{9}$:

$d = \frac{4d}{9} + 160$

$d - \frac{4d}{9} = 160$

$\frac{5d}{9} = 160$

$d = \frac{160(9)}{5}$

$d = 288$

Pablo lives 288 miles away from the mountains.

You can learn more about the relation between velocity, distance and time at https://brainly.com/question/24316569